Abstract: The two-dimensional $J$-$J^\prime$ dimerized quantum Heisenberg model is
studied on the square lattice by means of (stochastic series expansion) quantum
Monte Carlo simulations as a function of the coupling ratio
\hbox{$\alpha=J^\prime/J$}. The critical point of the order-disorder quantum
phase transition in the $J$-$J^\prime$ model is determined as
\hbox{$\alpha_\mathrm{c}=2.5196(2)$} by finite-size scaling for up to
approximately $10 000$ quantum spins. By comparing six dimerized models we
show, contrary to the current belief, that the critical exponents of the
$J$-$J^\prime$ model are not in agreement with the three-dimensional classical
Heisenberg universality class. This lends support to the notion of nontrivial
critical excitations at the quantum critical point.